Ogawa has defined sets of
Weierstrass points of a holomorphic vector bundle on a compact complex manifold.
We generate nontrivial examples of such sets of Weierstrass points by considering the
canonical bundle on a product of Riemann surfaces.
In the first section, we review Ogawa’s definition and some classical facts about
Weierstrass points on Riemann surfaces. In §2, we prove our theorems and consider
an example to illustrate the proofs. Finally, we remark that a connection between
Weierstrass points on a Riemann surface and fixed points of a periodic automorphism
does not seem to extend to higher dimensions.
We wish to thank Pierre Conner for helpful conversations and Roy Ogawa for
useful communications.
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